nll_exposed_infected function

Negative log-likelihood function: exposed-infected

Function returning negative log-likelihood (nll) for patterns of mortality in infected and control treatments, where the infected population harbours an unobserved proportion of hosts that were exposed to infection, but did not become infected.

nll_exposed_infected(
  a1 = a1,
  b1 = b1,
  a2 = a2,
  b2 = b2,
  p1 = p1,
  data = data,
  time = time,
  censor = censor,
  infected_treatment = infected_treatment,
  d1 = "Weibull",
  d2 = "Weibull"
)

Arguments

• a1, b1: location and scale parameters for background mortality
• a2, b2: location and scale parameters for mortality due to infection
• p1: unobserved proportion of hosts exposed to infection and infected; 0 <= p1 <= 1
• data: name of data frame containing survival data
• time: name of data frame column identifying time of event; time > 0
• censor: name of data frame column idenifying if event was death (0) or right-censoring (1)
• infected_treatment: name of data frame column identifying if data are from an infected (1) or uninfected (0) treatment
• d1, d2: names of probability distributions chosen to describe background mortality and mortality due to infection, respectively'; both default to the Weibull distribution

Returns

numeric

Details

This function returns the nll based on five parameters, the location and scale parameters for background mortality and mortality due to infection, respectively, plus a parameter for the proportion of hosts that became infected when exposed to infection.

Examples

# check column names in head of data frame with data to analyse
    head(data_parker)

# step #1: prepare nll function for analysis
    m01_prep_function <- function(a1 = a1, b1 = b1, a2 = a2, b2 = b2, p1 = p1){
      nll_exposed_infected(
        a1 = a1, b1 = b1, a2 = a2, b2 = b2, p1 = p1,
        data = data_parker,
        time = t,
        censor = censored,
        infected_treatment = g,
        d1 = "Frechet",
        d2 = "Weibull")
        }

# step #2: send 'prep_function' to mle2 for maximum likelihood estimation
    m01 <- mle2(m01_prep_function,
             start = list(a1 = 2.5, b1 = 1, a2 = 2, b2 = 0.5, p1 = 0.5)
             )

    summary(m01)

# model setting lower & upper bounds to parameter estimates
  # including 0 < p1 < 1
    m02 <- mle2(m01_prep_function,
             start = list(a1 = 2.5, b1 = 1.2, a2 = 1.9, b2 = 0.16, p1 = 0.48),
             method = "L-BFGS-B",
             lower = c(a1 = 0, b1 = 0, a2 = 0, b2 = 0, p1 = 0),
             upper = c(a1 = Inf, b1 = Inf, a2 = Inf, b2 = Inf, p1 = 1),
             )

    summary(m02)

See Also

nll_two_inf_subpops_obs

nll_two_inf_subpops_unobs